Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Design Automation and Design Space Exploration for Quantum Computers

A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by recent advances in reversible logic synthesis, we synthesize arithmetic circuits using classical design automation flows and tools. The combination of classical and reversible logic synthesis enables the automatic design of large components in reversible logic starting from well-known hardware description languages such as Verilog. As a prototype example for our approach we automatically generate high quality networks for the reciprocal $1/x$, which is necessary for quantum linear systems algorithms.Comment: 6 pages, 1 figure, in 2017 Design, Automation & Test in Europe Conference & Exhibition, DATE 2017, Lausanne, Switzerland, March 27-31, 201

Application of Permutation Group Theory in Reversible Logic Synthesis

The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits consisting of gates from the NCT library is described. An algorithm for gate complexity reduction, based on equivalent replacements of gates compositions, is introduced. A new approach for combining a group-theory-based synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is described. Experimental results are presented to show that the proposed synthesis techniques allow a reduction in input lines count, gate complexity or quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016 conferenc

Synthesis of Linear Reversible Circuits and EXOR-AND-based Circuits for Incompletely Specified Multi-Output Functions

At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n2/log2n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed. In this work, the GF(2) logic theory used in EPOE is expanded and the concept of an EXOR-AND product transform is introduced. Because of the generality of this logic theory, it is adapted to EXOR-AND-OR, or SPOE, synthesis. Three heuristic spectral logic synthesis algorithms are introduced, implemented in a program called XAX, and compared with previous work in classical logic circuits of up to 26 inputs. Three linear reversible circuit methods are also introduced and compared with previous work in linear reversible logic circuits of up to 100 inputs

Test of a majority-based reversible (quantum) 4 bits ripple-carry adder in adiabatic calculation

Quantum computing and circuits are of growing interest and so is reversible logic as it plays an important role in the synthesis of circuits dedicated to quantum computation. Moreover, reversible logic provides an alternative to classical computing machines, that may overcome many of the power dissipation problems in the near future. As a proof of concept we designed and tested a reversible 4 bits ripple-carry adder based on a do-spy-undo structure. This paper presents some performances obtained with such a chip processed in standard 0.35 μm CMOS technology and used in real reversible calculation (in this study, computations are performed in both directions such that addition and subtraction are made reversibly with the same chip). We also discuss the superiority of using adiabatic signals over classical rectangular pulses when using dual-line pass-transistor logic gates. Adiabatic signals allow the signal energy stored on the various capacitances of the circuit to be redistributed rather than being dissipated as heat. Finally, we show that adiabatic signals allow to avoid calculation errors introduced by the use of conventional rectangular pulses and allow to drastically reduce the number of pulse resynchronization in large circuits. Index Terms—reversible computation, design, implementation, pass-transistor logic, ripple-carry adder, Spectre simulation, quantum computation, adiabatic signal, test and measuremen